-
Internationally-Tradable Permits Can Be Riskier for a Country
than an Internally-Imposed Carbon Price
September 2015Discussion Paper 15-65
[email protected]
http://heep.hks.harvard.edu
Harvard Environmental Economics ProgramD E V E L O P I N G I N N
O VAT I V E A N S W E R S T O T O D AY ’ S C O M P L E X E N V I R
O N M E N TA L C H A L L E N G E S
Martin L. WeitzmanHarvard University
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Internationally-Tradable Permits Can
Be Riskier for a Country than an
Internally-Imposed Carbon Price
Martin L. Weitzman
Harvard University
-
The Harvard Environmental Economics Program
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Acknowledgements
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HEEP enjoys an institutional home in and support from the
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Citation Information
Weitzman, Martin L. “Internationally-Tradable Permits Can Be
Riskier for a Country than an
Internally-Imposed Carbon Price.” Discussion Paper 2015-65.
Cambridge, Mass.: Harvard
Environmental Economics Program, September 2015.
The views expressed in the Harvard Environmental Economics
Program Discussion Paper Series are
those of the author(s) and do not necessarily reflect those of
the Harvard Kennedy School or of
Harvard University. Discussion Papers have not undergone formal
review and approval. Such papers
are included in this series to elicit feedback and to encourage
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-
1 Introduction: Negotiating Prices vs. Negotiating
Quantities
The world is currently mired in what has aptly been called
global warming gridlock.1 The
core problem confronting the economics of climate change is an
inability to overcome the
obstacles associated with free riding on a very important
international public good. The
‘international’part is significant. Even within a nation, it can
be diffi cult to resolve public
goods problems. But at least there is a national government,
with some governance struc-
ture, able to exert some control over externalities within its
borders. With climate change
there is no overarching international governance mechanism
capable of coordinating the ac-
tions necessary to overcome the problem of free riding. Instead,
instruments of control (like
prices or quantities) must be negotiated among sovereign
nation-states. Negotiators here
are playing a game in which self-interested strategies are a
crucial consideration. It turns
out that negotiating rules define an important part of the game,
and can thereby change
self-interest, for better or for worse.
Two basic proposals for controlling carbon dioxide emissions
have been the subject of a
lively debate among economists. The first, price-based, approach
promotes an internationally
harmonized carbon price (or tax), the proceeds from which are
nationally retained and in-
ternally distributed as lump-sum payments (or used domestically
to offset other taxes). The
second, quantity-based, approach promotes an international
cap-and-trade regime where, for
simplicity here, the initial permits are distributed for free.2
The advantages and disadvan-
tages of the two approaches have by this time been vetted and
compared in a voluminous
literature.3
It has often been noted in this literature that the revenues
generated from an interna-
tionally harmonized cap-and-trade system flow as visible
external transfer payments across
national borders, which might be less easily tolerated by
countries required to pay other
1Global Warming Gridlock is the title of a book by David Victor
(2011), who popularized the phrase.2If permits were auctioned, the
distinction between a quantity-based system and a price-based
system
becomes blurrier, but a softened version of the basic point of
this paper would remain.3Rather than here listing scores of papers
with varying viewpoints, for an elaborate recent overall
summary
review of carbon taxes vs. cap-and-trade see Goulder and Schein
(2013) (and the many further referencesthey cite). Their
comprehensive survey indicates that, although the two options are
equivalent over moredimensions than often are recognized, in the
final analysis exogenous emissions pricing has a number ofimportant
attractions over pure cap and trade. They find it noteworthy that a
carbon tax seems to scorebetter along the dimensions where the
advantages or disadvantages are unambiguous. On the other
side,Gollier and Tirole (2015) make a recent case favoring a
quantity-based approach. I personally have favoreda price-based
approach for several reasons: in large part because stability of
carbon prices is very importantfor consumers and investors.
However, in this paper I want to present a new argument based on a
relatedbut different idea that cap-and-trade is riskier for an
individual nation-state than the corresponding priceinstrument even
when the risk comes only from country-specific idiosyncratic
shocks.
2
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countries large sums of taxpayer-financed money to buy permits.
Where it has been noted,
this argument has typically been invoked verbally and informally
(usually to the detriment
of tradable permits relative to an internationally harmonized
self-imposed price or tax).
In a recent paper, Cramton, Ockenfels, and Stoft (2015) have
provided a brief suggestive
numerical example of the phenomenon.4
The purpose of this paper is to compare formally an
internationally-tradeable permits
system with its “twin”uniform carbon-price system. I am here
making a “prices vs. quan-
tities”type comparison5 as it pertains to the welfare of an
individual country (as opposed to
the welfare of the entire world). It is important to bear in
mind throughout the paper that
the “prices vs. quantities”type welfare comparisons here are
entirely from the perspective
of an individual nation-state, and do not (necessarily) concern
worldwide well being.
To ensure a level playing field, I initially calibrate the two
twin price and quantity instru-
ments to be welfare-equivalent for a country in a deterministic
setting. While both price
and quantity instruments then have identical consequences under
perfect certainty, outcomes
can differ substantially under uncertainty. In particular, when
uncertainty takes the form of
idiosyncratic country-specific abatement-cost shocks, then
internationally tradable permits
expose a country to greater risk than imposing a uniform carbon
price whose tax proceeds
are domestically retained. This result is shown formally in a
very simple model that trans-
parently exposes the core argument. Some suggestive implications
are discussed. I argue
that this relative-riskiness result may be a pertinent
consideration in choosing between ne-
gotiated price-based approaches and negotiated quantity-based
approaches for controlling
worldwide carbon emissions.
2 The Model with Perfect Certainty
The unit of analysis here is some representative carbon-emitting
nation. The model in this
and the next section is completely deterministic. However, in
order to be able to concentrate
later on country-specific idiosyncratic uncertainty, I
effectively assume that I can perform
standard partial-equilibrium welfare analysis for this
representative nation. I believe that
the insights from the stochastic version of this simple core
model survive many further
complications, including the introduction of
non-country-specific general uncertainty that
affects all nations.4While illuminating and inspiring, their
example, in my opinion, does not constitute a formal model of
what I think may be an important phenomenon in deciding which
instruments are more easily negotiatedamong countries. Thus, I
acknowledge the brief numerical-verbal example of Cramton,
Ockenfels, and Stoft(2015) as an inspiration for the present
paper.
5In the spirit of Weitzman (1974), but here at the level of an
individual nation-state.
3
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Let Q here stand for the “good”of carbon dioxide abatement of
this representative nation
from some initial position. (Note that the “good”of abatement is
essentially the negative
of the “bad”of emissions.)
The marginal cost of carbon abatement for this nation is given
by the linear function
C ′(Q) = a+ bQ, (1)
where a and b are given positive constants.
Let P be an exogenously-imposed price of carbon abatement (or
emissions). When
the country maximizes profits by setting marginal cost (1) equal
to price, the resulting
“abatement supply function”is
Q(P ) =P − ab
. (2)
This completes the sparse description here of the representative
nation in the completely
deterministic case.
3 Imposing a Level Playing Field
Continuing with the case of the completely deterministic model
of the previous section, I
assume that there are two alternative ways to attain some given
level of abatement (or
emissions). These two contrasting approaches correspond to a
price instrument and a
quantity instrument.
On the price-instrument side, suppose there is a worldwide
harmonized price P̂ on carbon
emissions that a nation imposes on itself, but the tax receipts
from which are internally
retained in the nation. The tax receipts are distributed within
the nation as lump sum
payments, or they could be used to relieve the burdens of other
taxes. Either way, I assume
that the self-imposed nationally-rebated tax of P̂ is revenue
neutral and the tax-and-rebate
payments constitute an internal transfer that does not represent
by itself a net gain or net
loss of real welfare for the nation.
On the quantity-instrument side I assume that the
initially-assigned number of national
permits in a cap-and-trade system (expressed in abatement units)
is Q̂, which permits are
freely distributed to the nation.
For comparability, the international equilibrium price of
tradable carbon permits is also
P̂ . A level playing field for this country-based “prices vs.
quantities”comparison is imposed
by the condition that
P̂ = a+ bQ̂ (3)
4
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or, equivalently,
Q̂ =P̂ − ab
. (4)
Some reflection on this deterministic level-playing-field
calibration (3), (4) reveals that,
for a cap-and-trade regime, the nation’s net purchase (or sale)
of tradeable permits is zero.
Thus, as might be expected here within a deterministic setting,
the nation is completely
indifferent whether the internally-imposed tax is P̂ in a
price-based system or the initially-
assigned free permits are Q̂ in a quantity-based system. We are
encountering here an
instance of the basic duality that in a comparable deterministic
setup with full information
there is no difference between the two instruments. Thus, the
“prices vs. quantities”debate
in this twin deterministic setup results in a draw. The above
concept of a “level playing
field”in terms of identical deterministic outcomes under the two
instruments has heuristic or
intuitive appeal (at least for me). Unfortunately, I cannot
provide here, within this partial
equilibrium framework, a more rigorous justification for using
(3), (4) as a point of departure
for what follows.
The next question to be addressed is what happens in the
presence of uncertainty. In this
case a major difference will emerge in risk-bearing under the
two otherwise-twinned systems.
4 Idiosyncratic Country-Specific Uncertainty
Idiosyncratic country-specific abatement-cost uncertainty is
modeled here as follows. Let X
be a random variable representing an additive shock to the
marginal cost function (1) with
known distribution. Let x be a realization of the random
variable X. Then the marginal
cost function (given the realization x) is
C ′(Q | x) = a+ bQ+ x. (5)
Thus, “high”values of x are “bad”for the country, while
“low”values of x are “good”
for the country. The additive shock X is presumed to have a
“neutral”effect on marginal
cost in the sense that (without loss of generality) it is
assumed that its expected value is
zero:
E[X] = 0. (6)
Initially, during negotiations but before the uncertainty is
resolved, the country accepts
either the assigned price P̂ in the price system, or the initial
quantity assignment Q̂ in the
cap-and-trade quantity system, where (3), (4) hold.
5
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Then, after the uncertainty is resolved, comes a longish
reaction period of, say, 10 years
or so. After the uncertainty is resolved (for analytical
convenience at the beginning of
the reaction period), then during the entire reaction period the
country is stuck with the
consequences of a quasi-fixed instrument until the next
negotiating period. During the
reaction period, the realized marginal cost has been shifted by
amount x. Thus, the country
must make a decision under uncertainty between choosing the
price P̂ in the price system
or choosing the initial quantity assignment Q̂ in the
cap-and-trade quantity system while X
is still a random variable, but thereafter the country must live
with the consequences of its
realization x of X throughout the reaction period.
For simplicity, I am assuming that after the idiosyncratic shock
X has been realized to be
x, the nation is stuck with its initial assignment of price P̂
throughout the reaction period.
In the price system, this merely reflects the truism that the
internally-assigned price remains
P̂ throughout the reaction period. In the quantity system, I
assume for simplicity here that
the post-shock international equilibrium price of emissions
permits remains P̂ . I can make
more complicated assumptions about the impacts of uncertainty,
but the setup here focuses
sharply on the main message in a form that the model can deliver
most clearly.6
5 The Price-Instrument Reaction
In a price-instrument reaction to realization x, the nation will
abate to the level where
the post-shock marginal abatement cost (5) equals the imposed
price P̂ . This results in
abatement quantity
Q(P̂ | x) = P̂ − a− xb
= Q̂− xb. (7)
From (7), the change in abatement level Q per unit change in x
is −1/b. Therefore,the net gain of government revenue ∆R from
taxing emissions at price P̂ for realization x
(compared with x = 0) is
∆R(x) = P̂ ×(xb
), (8)
which also represents the net total loss of revenue to carbon
emitters. However, the extra
net revenues ∆R given by (8) do not constitute a genuine change
of real welfare, because
they are presumed to be recycled in a revenue-neutral fashion
(via lump-sum transfers or6For example, if the international
equilibrium price of emissions permits increases with x (say
because
cost shocks are correlated across countries), a symbol- and
algebra-intensive extension of the model mightbe used to show under
reasonable assumptions that the quantity-based tradeable-permits
system exposesthe nation to even greater risk than occurs in the
analysis of the current paper. Thus, an assumptionof correlated
cross-country abatement-cost shocks will tend to increase the
risk-bearing differences in thecountry-level “prices vs.
quantities”analysis of this paper. A rigorous treatment of this
extension is moreproperly the subject of future research.
6
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in relief of other equivalent taxes). Effectively, the nation is
simultaneously collecting and
rebating additional revenues of net amount ∆R, which is an
internal transfer that leaves the
real overall welfare level the same as before.
However, there is a real loss (or gain) from the increased (or
decreased) cost of compliance.
The real net cost loss from realization x (compared to x = 0)
is
Lp(x) =
∫ x0
C ′(Q(P̂ | X)) dX. (9)
Substituting from (5) and (7) into (9) gives the expression
Lp(x) =
∫ x0
[a+ b
(P̂ − a−X
b
)+X
]dX. (10)
Cancelling redundant terms in (10) and carrying out the
integration yields
Lp(x) = P̂ x. (11)
6 The Quantity-Instrument Reaction
Under cap-and-trade, the nation has been allocated allowance
permits that cover only abate-
ment of amount Q̂. Therefore, to be in compliance with the
tradable-permits quantity man-
date, the nation facing marginal cost shock realization x must
purchase from (when x > 0,
or sell to when x < 0) the outside world market[Q̂−Q(P̂ |
x)
]permits at the postulated
post-shock world equilibrium price P̂ . This amounts to a real
transfer loss of national
income in net amount
Lt(x) = P̂ ×[Q̂−Q(P̂ | x)
], (12)
consisting of real resources (in money terms) externally
transferred abroad to buy permits.
Using expression (7), the real national income transfer-loss
(12) can be rewritten in the
simpler reduced form
Lt(x) = P̂ ×x
b(13)
Additionally, there is a real loss (or gain) from the increased
(or decreased) cost of
compliance. The real net cost loss from realization x (compared
to x = 0) is the same under
the quantity system as it is under the price system, namely
Lp(x) = P̂ x from equation (11).
7
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The total real net loss of welfare under the quantity system is
therefore
Lq(x) = Lp(x) + Lt(x), (14)
which, making use of (11) and (13), can be rewritten in the
reduced form
Lq(x) =
(1 +
1
b
)P̂ x. (15)
7 The Basic Country-Level Welfare Comparison
Let us compare the price-based loss of welfare Lp(x) in equation
(11) with the quantity-based
loss of welfare Lq(x) in equation (15). Because E[X] = 0, the
expected net loss of welfarehas the same value of zero in both
systems, so that7
E[Lq(X)] = E[Lp(X)] = 0. (16)
But, because of the extra term P̂ x/b in (15), the
quantity-based loss of welfare Lq(x)
has greater variability than the price-based loss of welfare
Lp(x) given by (11). (Note that
the probability distribution of Lq(X) with variance V[Lq(X)] =
(1 + 1/b)2 P̂ 2V[X] is amean-preserving spread of the probability
distribution of Lp(X) with variance V[Lp(X)] =P̂ 2V[X]). Thus,
V[Lq(X)] = V[Lp(X)] +(
2
b+
1
b2
)P̂ 2V[X] (17)
From (16) and (17), it is fair to say that, while both systems
have the same expected
net loss (of zero), tradable permits expose a country to the
additional external risk of a
real loss (or gain) of P̂ x/b, while under a price commitment to
an internally-rebated carbon
price (or tax) the nation merely keeps its price set to P̂ , as
if no foreign transfers occurred.
This real-welfare comparison is the basis for the claim given by
the title of this paper that
“internationally-tradable permits can be riskier for a country
than an internally-imposed
carbon price.” The reason here is just about as simple as an
answer to the question: “Which
of the following two alternatives would a risk-averse country
prefer: to charge itself an
additional carbon-tax revenue P̂ x/b that is internally rebated,
or to be levied the same
exact carbon-tax revenue P̂ x/b that is externally paid out to
the rest of the world?”. Thus,
from the thicket of algebra emerges a very simple intuitive
comparison.
Note that I am effectively resorting to an argument outside of
the formal model of the
7If P (Q) were convex, instead of linear, the expected welfare
would be higher under the price system thanunder the quantity
system.
8
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paper to make the commonsense observation that the quantity
instrument is riskier than the
price instrument because Lq(X) is more variable than Lp(X),
while having the same mean.
I am thus not treating risk in a micro-foundational way that is
fully integrated with the rest
of the model of this paper. I also omit considerations of
futures hedging markets, forward
purchases and sales of permits, puts and calls on permit prices,
and so forth, which, at least
theoretically, might conceivably lessen (or, perhaps increase)
variability.8
Suppose the world-equilibrium price of tradable permits is
positively correlated with the
bad country-specific outcomes. In other words, when the country
wants to buy more permits
to cover increased emissions (because x > 0), so do other
countries, thereby raising the world-
equilibrium price of permits. Exact results depend on how this
aspect is modeled, but the
commonsense conclusion would seem to favor an expression that is
even more variable than
(15). Thus, with an uncertain world price of tradable quotas the
quantity instrument is
likely to be riskier by an even larger margin (when compared
with the the constant-price
instrument P̂ ).9 For purposes of the present paper, an exact
investigation of this phenomenon
remains an area of future research.
8 Concluding Remarks on the Value of Stability in
Real-Revenue Transfers
If there were a single world government with the worldwide power
to levy targets and redis-
tribute taxes and transfers, then what, in this paper,
constitutes external transfer payments
across national boundaries (from a cap-and-trade system), would
net out to zero worldwide.
This is essentially the setup of my earlier paper “Prices vs.
Quantities”(Weitzman (1974)),
where there is a single overarching government that, in
principle, might choose between
the two instruments by using the formula in that article for the
“comparative advantage of
prices over quantities.”However, in a world consisting of
independent nation-states, prices
and quantities are not assigned by an overarching (world)
government; they must instead be
negotiated among sovereign entities that are inclined to free
ride on an international public
good.
It is in the context of such international negotiations that the
results of this paper might
be most relevant. I believe that the idea that internationally
tradeable permits can be riskier
8I am not sure but that derivatives markets for pollution
permits might possibly backfire in practice,with bad consequences
including public blaming of “speculators.” Laffont and Tirole
(1996) propose animaginative mechanism where tradable permits have
put options with various strike prices. They show thatsuch a
mechanism in principle deals effectively with the progressive
resolution of uncertainty over time.
9McKibbin, Morris, and Wilcoxen (2009) compare numerically the
performance of various instruments inthe presence of unexpected
macroeconomic shocks.
9
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for a country than an internally-imposed carbon price
translates, via risk aversion, into an
argument that it may be easier for the world to negotiate a
uniform quasi-fixed carbon price,
which is internally retained, than to negotiate an initial
assignment of tradeable permits.10
It is not going to be easy to negotiate a uniform carbon price,
but I believe that the main
result of this paper might be informally interpreted as
suggesting that lower side payments
may be required of a “green fund”compensation mechanism to
encourage a uniform carbon
price than is required to induce compliance in a nationally
riskier cap-and-trade system.
An internationally harmonized but domestically retained carbon
price will require mea-
surement, verification, and most importantly, serious sanctions
for enforcement (as well as,
most likely, some green fund transfers). One constructive idea
is for a coalition of willing
nations to form a “climate club”by agreeing to impose on
themselves a uniform price of
carbon. Any country willing to join the club must price carbon
at the agreed-upon price.
Nations choosing to remain outside the club are forced to pay
some agreed-upon uniform
ad-valorem border tax on goods and services that the club
members import from non-club
members.11 Another possibility is to empower a “World Climate
Assembly”where nations
vote on the desired level of a uniform carbon price on the basis
of one-person one-vote ma-
jority rule.12 Where there is a will, there is a way. The
purpose of this paper is merely
to suggest that countries, because they are exposed to less
risk, may find it relatively easier
to comply with an internationally-harmonized but
nationally-collected price than to comply
with an analogous cap-and-trade system that is inherently
riskier for them.
References
[1] Cramton, Peter, Axel Ockenfels, and Steven Stoft (2015). “An
International Carbon-
Price Commitment Promotes Cooperation.” Economics of Energy
& Environmental
Policy, forthcoming.
[2] Gollier, Christian, and Jean Tirole (2015). “Negotiating
Effective Institutions Against
Climate Change.” Economics of Energy & Environmental Policy,
forthcoming.
10I have tried to argue previously, on different grounds of
providing a focal point for a common commitmentand lower
transactions costs, that negotiating a uniform carbon price can
help to internalize the globalwarming externality by empowering a
“countervailing force”against free riding. See Weitzman
(2014).11This “climate club” idea is the brainchild of William
Nordhaus, who shows numerically that an ad-
valorem border tariff of 4% on imports from non-club members
would be suffi cient for all countries to wantto join the climate
club by agreeing to impose on themselves an internally-retained tax
of $25 per ton ofemitted carbon dioxide. See Nordhaus (2015).12This
voting idea is mooted in Weitzman (2014), who shows that voting on
a harmonized carbon price
gives voters incentives to employ countervailing force against
free riding.
10
-
[3] Goulder, Lawrence H., and Andrew R. Schein (2013). “Carbon
Taxes vs. Cap and Trade:
A Critical Review.” Climate Change Economics 4(3): 1-28.
[4] Laffont, Jean-Jacques, and Jean Tirole (1996). “Pollution
permits and compliance strate-
gies.” Journal of Public Economics 62: 85-125.
[5] McKibbin, Warwick, Adele Morris, and Peter Wilcoxen (2009).
“Expecting the Unex-
pected: Macroeconomic Volatility and Climate Policy,”in J. Aldy
and R. Stavins (eds),
Architecture for Agreement: Addressing Global Climate Change in
the Post-Kyoto World.
Cambridge University Press, pp 185-208.
[6] Nordhaus, William D. (2015). “Climate Clubs: Designing a
Mechanism to Overcome
Free-riding in International Climate Policy.”American Economic
Review 105 (4); 1339-
1370.
[7] Victor, David (2011). Global Warming Gridlock. Cambridge:
Cambridge University
Press.
[8] Weitzman, Martin L. (1974). “Prices vs. Quantities.” Review
of Economic Studies 41,
4: 477-491.
[9] Weitzman, Martin L. (2014). “Can Negotiating a Uniform
Carbon Price Help to Inter-
nalize the Global Warming Externality?” Journal of the
Association of Environmental
and Resource Economists 1(1/2): 29-49.
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